4 Answers
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It is a common misconception that something in (Low Earth) orbit (like the ISS) is far away. This is not the case -- orbit is more about going sideways really fast than it is about "being up". (xkcd -- Orbital Speed)

The ISS has perigee at 402 km and apogee at 409 km ([1]). Unless you're further north / south than 51 degrees (The ISS' orbital inclination), at some point the ISS will be directly overhead, i.e. a bit over 400 km away from you.

Compared to that, the oceanic pole of inaccessibility...

...lies in the South Pacific Ocean, 2,688 km (1,670 mi) from the nearest lands. ([2]).

So, allowing for some ship being closer while the ISS is on the other side of the earth, at least some of the time the claim is true, and quite possibly by a comfortable margin.

You can possibly find places on land where the ISS crew is closer to you than the next person on earth...

A picture gives a sense of proportion. To the Earth, a rock diameter 13000km, clings a wisp of atmosphere. The troposphere, where everyone has ever breathed, is thinner than 20km. Above, space. The Internal Space Station orbits at about 400 km.

THE THIN BLUE LINE: Earth’s thin atmosphere is all that stands between life on Earth and the cold, dark void of space. Our planet's atmosphere has no clearly defined upper boundary but gradually thins out into space. The layers of the atmosphere have different characteristics, such as protective ozone in the stratosphere, and weather in the lowermost layer. The setting Sun is also featured in this image, which was photographed by the crew of the International Space Station in 2008.

Yes, actually, I can. West Southwest of Australia. 800 km isn't actually all that much on the scale of the oceans. I sized Google maps to about the same scale and used the measurement tool to confirm that some of the holes North of 51 deg South are indeed greater than 800 km in diameter. Nevertheless, this map is an interesting find.
– reirabMay 19 '17 at 21:45

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How many of those ships without transponders operate on the high seas in sparse areas of the Southern Indian Ocean, though? Aircraft flights there are quite rare. There's just not much reason to fly there. Inhabited islands in the Southern Indian Ocean are also very few and far between (much farther than 800 km.) Right now, for example, FlightRadar24 shows exactly 1 flight over the entire Southern part of the Indian Ocean.
– reirabMay 19 '17 at 22:01

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There seems to be a worldwide allergy to sensible map projections, but the far south Atlantic and far south Indian Ocean meet your criteria. (According to the map, the north Atlantic and the South China Sea do as well, but I'm certain those are false-positives.)
– MarkMay 19 '17 at 22:44

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@reirab Note that the image caption text (in German!) says that a few regions are not yet covered by this helix antenna, and that is why we do not see any dots in e.g. the German Bight where there are in reality a very large number of ships at any time. So it is clear that the image does not show all ships, for various reasons. So it is not "obvious" that you can stand somewhere within the 51st latitudes and have no ships or settlements within 400 km from you. So, 400 km is not much compared to the size of the oceans, but there are many ships!
– Jeppe Stig NielsenMay 22 '17 at 8:04

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@JanDvorak However, since it is at latitudes​ way over 51 degrees North, it does not qualify in the strict version of the question. The ISS will never come near the Norwegian Sea.
– Jeppe Stig NielsenMay 22 '17 at 15:46

With the space station up about 200 miles. Guess here. but close that is considered low orbit. There was a day last year that there were no cargo ships in the Atlantic ocean last year. It need not be remote ocean. In the S Pacific were I live. It is sometimes called the big lonely out there. So yes.

Some of the information contained in this post requires additional references. Please edit to add citations to reliable sources that support the assertions made here. Unsourced material may be disputed or deleted.

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We're looking for answers with citations. Not to say that you're wrong, but you should cite the 200 miles to the space station claim and the claim that a location is more than 200 miles from other people. Even the no cargo ships in the Atlantic claim should be cited,
– BrythanMay 20 '17 at 3:37